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Khoshtip
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Joined: November 17th, 2006, 2:08 pm

Skews to use in local volatility pricing

June 5th, 2012, 1:52 pm

Hi,The question is with regards to what implied vol skews to include in pricing using local volatility. Assuming I would like to price an option maturing at T, looking in the the litterature the conclusion seems to be that one has to use vol points/vanilla prices for various maturities. The last maturities for calibration options being from the market skew after the option expiry at T.To make the case easy lets say our option maturity T coincides with an exchange maturity date.I have compared prices for barrier options usingA) the full information set, i.e. all the skews between 0 to TB) only the calibration options at T (i.e. the maturity skew is projected backwards in time) The prices are very very similar!!!I know that the skews at T contain information about the volatiliy behaviour between 0 to T, some sort of average behaviour since the total variance must be the same. The question is how good of an approximation this approach is and when this approach reaches its limit?Would appreciate any hints or papers treating the issue.Thanks in advance!
 
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secret2
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Joined: July 28th, 2010, 10:29 pm

Skews to use in local volatility pricing

June 5th, 2012, 3:36 pm

Hi Khoshtip.How exactly did you do it "using only the calibration options at T (i.e. the maturity skew is projected backwards in time)"?
 
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Khoshtip
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Joined: November 17th, 2006, 2:08 pm

Skews to use in local volatility pricing

June 6th, 2012, 10:44 am

I used the volatiltiy skew from the option expiry at T for all the time points between now and expiry.I.e. if my ATM vol at T is 25% this value was used for now<t<T fro the ATM strike...and 90ATM% vol at T is 28%, then this value was used for now<t<T for this strikeCheers,K